Noticing Patterns

The key to solving these problems is to notice patterns or properties. Encouraging students to organise their work in a systematic way will allow them to notice what might not otherwise be obvious.

Summing Consecutive Numbers

Age 11 to 14
Challenge Level

This problem offers a simple context for students to explore, make generalisations and prove conjectures, working numerically and algebraically.

1 Step 2 Step

Age 11 to 14
Challenge Level

This problem is inaccessible without looking at simpler cases, and thus helps students to see the value of specialising in order to generalise.

Pick's Theoremlive

Age 14 to 16
Challenge Level

This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

What's Possible?

Age 14 to 16
Challenge Level

As well as introducing the difference of two squares, this problem allows students to explore, conjecture and use algebra to justify their results.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.